On the rate of convergence of Noor, SP and P-iterations for continuous functions on an arbitrary interval
Abstract
In this paper, we first give a necessary and sufficient condition for convergence of P-iteration to a fixed point of continuous functions on an arbitrary interval and prove equivalence of P-iteration, Noor and SP-iteration. We also compare the convergence speed of Noor, SP-iteration and P-iteration. It is proved that the P-iteration con verges faster than Noor and SP-iterations. Moreover, we also present numerical examples for the P-iteration to compare with the Noor and SP-iterations.
Copyright © 2019 Prayong Sainuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
P. Sainuan, On the rate of convergence of Noor, SP and P-iterations for continuous functions on an arbitrary interval, Adv. Fixed Point Theory 9 (2019), 45–68. https://doi.org/10.28919/afpt/3941
BibTeX
@article{Sainuan2019,
author = {Sainuan, Prayong},
title = {On the rate of convergence of Noor, SP and P-iterations for continuous functions on an arbitrary interval},
journal = {Adv. Fixed Point Theory},
volume = {9},
year = {2019},
pages = {45--68},
doi = {10.28919/afpt/3941}
}